What is 4/(x-7)-3/x <6 ?

The solution to 4/(x-7)-3/x (43+sqrt(2353))/(12)

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4/(x-7)-3/x <6

\frac{4}{x - 7} - \frac{3}{x} < 6

x < \frac{43 - 2353}{12} or 0 < x < 7 or x > \frac{43 + 2353}{12}

Interval Notation

(- \infty, \frac{43 - 2353}{12}) \cup (0, 7) \cup (\frac{43 + 2353}{12}, \infty)

Decimal Notation

x < - 0.45897 \dots or 0 < x < 7 or x > 7.62564 \dots

Solution steps

\frac{4}{x - 7} - \frac{3}{x} < 6

Rewrite in standard form

\frac{- 6 x ^{2} + 43 x + 21}{x ( x - 7 )} < 0

Factor

- 6 x^{2} + 43 x + 21 : - (x - \frac{43 + 2353}{12}) (x - \frac{43 - 2353}{12})

\frac{- ( x - \frac{43 + 2353}{12} ) ( x - \frac{43 - 2353}{12} )}{x ( x - 7 )} < 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x - \frac{43 + 2353}{12} ) ( x - \frac{43 - 2353}{12} ) ) ( - 1 )}{x ( x - 7 )} > 0 \cdot (- 1)

Simplify

\frac{( x - \frac{43 + 2353}{12} ) ( x - \frac{43 - 2353}{12} )}{x ( x - 7 )} > 0

Identify the intervals

x < \frac{43 - 2353}{12} or 0 < x < 7 or x > \frac{43 + 2353}{12}

16 n^{2} - 56 n + 49

1 - \frac{5}{3}

p^{2} + 17 p + 72

4 (2 z - 5) = - 4

- 2^{2} + y^{2} = 1

What is 4/(x-7)-3/x <6 ?
The solution to 4/(x-7)-3/x <6 is x<(43-sqrt(2353))/(12)\lor 0<x<7\lor x>(43+sqrt(2353))/(12)